Question

Tính

A= 2⁰ + 2¹ + 2² + 2³ +... +2¹⁰⁰

Answer 1

\(A=2^0+2^1+2^2+2^3+.......+2^{100}\)

\(2A=2\left(2^0+2^1+2^2+2^3+..........+2^{100}\right)\)

\(2A=2^1+2^2+2^3+2^4+.......+2^{101}\)
\(2A-A=\left(2^1+2^2+2^3+2^4+........+2^{101}\right)-\left(2^0+2^1+2^2+2^3+..........+2^{100}\right)\)\(2A=2^{101}-2^0=2^{101}-1\)

Answer 2

Ta có : $A=2^0+2^1+2^2+2^3+...+2^{100}$

$=>2A=2^1+2^2+2^3+2^4+...+2^{101}$

$=>2A-A=(2^1+2^2+2^3+...+2^{101})-(2^0+2^1+2^2+...+2^{100})$

$=>A=2^101-2^0=2^101-1$

Answer 3

\(A=2^0+2^1+2^2+.....+2^{100}\)

\(\Rightarrow2A=2^1+2^2+2^3+.......+2^{101}\)

\(\Rightarrow2A-A=\left(2^1+2^2+2^3+.....+2^{101}\right)-\left(2^0+2^1+2^2+.....+2^{100}\right)\)

\(\Rightarrow A=2^{101}-1\)

Chúc bạn học tốt!!!